Tautology

Description

WFF 'N PROOF is a logic game played with dice. Each die has six faces representing some subset of the possible symbols K, A, N, C, E, p, q, r, s, t. A Well-formed formula (WFF) is any string of these symbols obeying the following rules:

p, q, r, s, and t are WFFs
if w is a WFF, Nw is a WFF
if w and x are WFFs, Kwx, Awx, Cwx, and Ewx are WFFs.

The meaning of a WFF is defined as follows:

p, q, r, s, and t are logical variables that may take on the value 0 (false) or 1 (true).
K, A, N, C, E mean and, or, not, implies, and equals as defined in the truth table below.

Definitions of K, A, N, C, and E

w x	Kwx	Awx	Nw	Cwx	Ewx
1 1	1	1	0	1	1
1 0	0	1	0	0	0
0 1	0	1	1	1	0
0 0	0	0	1	1	1

A tautology is a WFF that has value 1 (true) regardless of the values of its variables. For example, ApNp is a tautology because it is true regardless of the value of p. On the other hand, ApNq is not, because it has the value 0 for p=0, q=1.

You must determine whether or not a WFF is a tautology.

Input

Input consists of several test cases. Each test case is a single line containing a WFF with no more than 100 symbols. A line containing 0 follows the last case.

Output

For each test case, output a line containing tautology or not as appropriate.

Sample Input

ApNp
ApNq
0

Sample Output

tautology
not

 1 //类似于后缀式求值；
 2 
 3 #include<stdio.h>
 4 #include<string.h>
 5 #include<stack>
 6 using namespace std;
 7 
 8 char ss[101];
 9 stack <int> st;
10 int flag;
11 
12 void check(int p, int q, int r, int s,int t)
13 {
14     while(!st.empty())
15         st.pop();
16     int a,b;
17     int len = strlen(ss);
18     for(int i = len-1; i >= 0; i--)
19     {
20         if(ss[i] == 'p')
21             st.push(p);
22         else if(ss[i] == 'q')
23             st.push(q);
24         else if(ss[i] == 'r')
25             st.push(r);
26         else if(ss[i] == 's')
27             st.push(s);
28         else if(ss[i] == 't')
29             st.push(t);
30         else if(ss[i] == 'K')
31         {
32             a = st.top();
33             st.pop();
34             b = st.top();
35             st.pop();
36             if(a == 1 && b == 1)
37                 st.push(1);
38             else st.push(0);
39         }
40         else if(ss[i] == 'A')
41         {
42             a = st.top();
43             st.pop();
44             b = st.top();
45             st.pop();
46             if(a == 0 && b == 0)
47                 st.push(0);
48             else st.push(1);
49         }
50         else if(ss[i] == 'N')
51         {
52             a = st.top();
53             st.pop();
54             if(a == 1)
55                 st.push(0);
56             else st.push(1);
57         }
58         else if(ss[i] == 'C')
59         {
60             a = st.top();
61             st.pop();
62             b = st.top();
63             st.pop();
64             if(a == 0 && b == 1)
65                 st.push(0);
66             else st.push(1);
67         }
68         else if(ss[i] == 'E')
69         {
70             a = st.top();
71             st.pop();
72             b = st.top();
73             st.pop();
74             st.push((a && b) || (!a && !b));
75         }
76     }
77     if(st.top() != 1)
78         flag = 0;
79 }
80 int main()
81 {
82     while(~scanf("%s",ss))
83     {
84         flag = 1;
85         if(strcmp("0",ss) == 0)
86             break;
87         for(int p = 0; p < 2; p++)
88             for(int q = 0; q < 2; q++)
89                 for(int r = 0; r < 2; r++)
90                     for(int s = 0; s < 2; s++)
91                         for(int t = 0; t < 2; t++)
92                             check(p, q, r, s, t);
93         if(flag == 1)
94             printf("tautology
");
95         else printf("not
");
96     }
97     return 0;
98 }

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